Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as translation equivariance in convolutional neural networks, and incorporation of new symmetry types is actively being studied. Yet, efforts to learn such invariances from the data itself remains an open research problem. It has been shown that marginal likelihood offers a principled way to learn invariances in Gaussian Processes. We propose a weight-space equivalent to this approach, by minimizing a lower bound on the marginal likelihood to learn invariances in neural networks resulting in naturally higher performing models.

Leveraging labelled data from multiple domains to enable prediction in another domain without labels is a significant, yet challenging problem. To address this problem, we introduce the framework DAPDAG (\textbf{D}omain \textbf{A}daptation via \textbf{P}erturbed \textbf{DAG} Reconstruction) and propose to learn an auto-encoder that undertakes inference on population statistics given features and reconstructing a directed acyclic graph (DAG) as an auxiliary task. The underlying DAG structure is assumed invariant among observed variables whose conditional distributions are allowed to vary across domains led by a latent environmental variable $E$. The encoder is designed to serve as an inference device on $E$ while the decoder reconstructs each observed variable conditioned on its graphical parents in the DAG and the inferred $E$. We train the encoder and decoder jointly in an end-to-end manner and conduct experiments on synthetic and real datasets with mixed variables. Empirical results demonstrate that reconstructing the DAG benefits the approximate inference. Furthermore, our approach can achieve competitive performance against other benchmarks in prediction tasks, with better adaptation ability, especially in the target domain significantly different from the source domains.

Emerging six generation (6G) is the integration of heterogeneous wireless networks, which can seamlessly support anywhere and anytime networking. But high Quality-of-Trust should be offered by 6G to meet mobile user expectations. Artificial intelligence (AI) is considered as one of the most important components in 6G. Then AI-based trust management is a promising paradigm to provide trusted and reliable services. In this article, a generative adversarial learning-enabled trust management method is presented for 6G wireless networks. Some typical AI-based trust management schemes are first reviewed, and then a potential heterogeneous and intelligent 6G architecture is introduced. Next, the integration of AI and trust management is developed to optimize the intelligence and security. Finally, the presented AI-based trust management method is applied to secure clustering to achieve reliable and real-time communications. Simulation results have demonstrated its excellent performance in guaranteeing network security and service quality.

We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of evidence represented by Gaussian random fuzzy numbers (GRFN's) and combined by the generalized product intersection rule, an operator that extends Dempster's rule to random fuzzy sets. The network output is a GRFN that can be summarized by three numbers characterizing the most plausible predicted value, variability around this value, and epistemic uncertainty. Experiments with real datasets demonstrate the very good performance of the method as compared to state-of-the-art evidential and statistical learning algorithms.

Political science research often requires constructing a race/ethnicity proxy variable for datasets that do not contain it, like voter registration files, lists of electoral candidates, or political donation records. Constructing such a proxy is an important step for conducting ecological inference in voting rights litigation (Barreto et al. [2019], Imai and Khanna [2016]), redistricting (DeLuca and Curiel [2022], Kenny et al. [2021]), and substantive research on the role of race/ethnicity in politics (Enos [2016], Enos et al. [2019], Grumbach and Sahn [2020]). The most common method for proxying race/ethnicity is Bayesian Improved Surname Geocoding (BISG), which uses Bayes' rule to compute a probability distribution over race/ethnicity categories conditional on a voter's surname and where they live (Elliott et al. [2008, 2009]). BISG has attained widespread popularity due to its parsimony, computational efficiency, and superior performance when compared to existing alternatives, namely spatial interpolation of Census racial-ethnic composition from Census geographies (Imai and Khanna [2016], Clark et al. [2021], Shah and Davis [2017]). While BISG performs well compared to the small suite of existing alternatives, it has not yet been benchmarked against machine learning (ML) models, which can produce race/ethnicity predictions from more flexible and potentially more accurate models. In this paper I present the results of such a benchmark. I train a range of machine learning models using voter registration data from Florida, Georgia, North Carolina, and a portion of California where voters self-report their race/ethnicity upon registration. The registries in these states contain over 26 million labelled observations, which equates to greater than a five percent non-representative sample of the United States electorate. I then compare BISG against predictions from these models made out-of-state.

A much studied issue is the extent to which the confidence scores provided by machine learning algorithms are calibrated to ground truth probabilities. Our starting point is that calibration is seemingly incompatible with class weighting, a technique often employed when one class is less common (class imbalance) or with the hope of achieving some external objective (cost-sensitive learning). We provide a model-based explanation for this incompatibility and use our anthropomorphic model to generate a simple method of recovering likelihoods from an algorithm that is miscalibrated due to class weighting.

Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and reinforcement learning models. Existing methods rely on the assumed structure and probabilities of certain system transitions. These assumptions may be incorrect, and may even be violated by an adversary who gains control of system components. In this paper, we develop a formal framework for adversarial robustness in systems modeled as discrete time Markov chains (DTMCs). We base our framework on existing methods for verifying probabilistic temporal logic properties and extend it to include deterministic, memoryless policies acting in Markov decision processes (MDPs). Our framework includes a flexible approach for specifying structure-preserving and non structure-preserving adversarial models. We outline a class of threat models under which adversaries can perturb system transitions, constrained by an $\varepsilon$ ball around the original transition probabilities. We define three main DTMC adversarial robustness problems: adversarial robustness verification, maximal $\delta$ synthesis, and worst case attack synthesis. We present two optimization-based solutions to these three problems, leveraging traditional and parametric probabilistic model checking techniques. We then evaluate our solutions on two stochastic protocols and a collection of Grid World case studies, which model an agent acting in an environment described as an MDP. We find that the parametric solution results in fast computation for small parameter spaces. In the case of less restrictive (stronger) adversaries, the number of parameters increases, and directly computing property satisfaction probabilities is more scalable. We demonstrate the usefulness of our definitions and solutions by comparing system outcomes over various properties, threat models, and case studies.

We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with an efficient message passing implementation, called UAMPMF. With proper priors imposed on the factor matrices, UAMPMF can be used to solve many problems that can be formulated as MF, such as non negative matrix factorization, dictionary learning, compressive sensing with matrix uncertainty, robust principal component analysis, and sparse matrix factorization. Extensive numerical examples are provided to show that UAMPMF significantly outperforms state-of-the-art algorithms in terms of recovery accuracy, robustness and computational complexity.

Deep Gaussian Process (DGP) as a model prior in Bayesian learning intuitively exploits the expressive power in function composition. DGPs also offer diverse modeling capabilities, but inference is challenging because marginalization in latent function space is not tractable. With Bochner's theorem, DGP with squared exponential kernel can be viewed as a deep trigonometric network consisting of the random feature layers, sine and cosine activation units, and random weight layers. In the wide limit with a bottleneck, we show that the weight space view yields the same effective covariance functions which were obtained previously in function space. Also, varying the prior distributions over network parameters is equivalent to employing different kernels. As such, DGPs can be translated into the deep bottlenecked trig networks, with which the exact maximum a posteriori estimation can be obtained. Interestingly, the network representation enables the study of DGP's neural tangent kernel, which may also reveal the mean of the intractable predictive distribution. Statistically, unlike the shallow networks, deep networks of finite width have covariance deviating from the limiting kernel, and the inner and outer widths may play different roles in feature learning. Numerical simulations are present to support our findings.

Studies show that Studies that cardiovascular diseases (CVDs) are malignant for human health. Thus, it is important to have an efficient way of CVD prognosis. In response to this, the healthcare industry has adopted machine learning-based smart solutions to alleviate the manual process of CVD prognosis. Thus, this work proposes an information fusion technique that combines key attributes of a person through analysis of variance (ANOVA) and domain experts' knowledge. It also introduces a new collection of CVD data samples for emerging research. There are thirty-eight experiments conducted exhaustively to verify the performance of the proposed framework on four publicly available benchmark datasets and the newly created dataset in this work. The ablation study shows that the proposed approach can achieve a competitive mean average accuracy (mAA) of 99.2% and a mean average AUC of 97.9%.